# A triangle has sides with lengths of 24 millimeters, 32 millimeters, and 43 millimeters. Is it a right triangle?

Dec 1, 2016

No.

#### Explanation:

You can check if a triangle is a right triangle if you know all three sides by using the formula:

${a}^{2} + {b}^{2} = {c}^{2}$

Where $a$ and $b$ are the two non-hypotenuse sides, and $c$ is the hypotenuse's length (the longest side of the triangle).

If the formula turns out to be true, then the triangle is a right triangle.
If it is not true, then it is not a right triangle.

${\left(24\right)}^{2} + {\left(32\right)}^{2} = 576 + 1024 = 1600$.
${\left(43\right)}^{2} = 1849$
$1600 \ne 1849$

Therefore, the triangle described is not a right triangle.

Dec 1, 2016

$1600 \ne 1849$ Therefore this is not a right triangle.

#### Explanation:

To determine if this is a right triangle you need to substitute the two legs of the triangle (24 and 32) and the hypotenuse (43) into the Pythagorean Theorem and see if both sides of the equation are equal. If they are it is a right triangle. If they are not equal this is not a right triangle.

The Pythagorean Theorem states:

${a}^{2} + {b}^{2} = {c}^{2}$

Substituting gives:

${24}^{2} + {32}^{2} = {43}^{2}$

Calculating gives:

$576 + 1024 = 1849$

$1600 \ne 1849$